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## Topic review (newest first)

irspow
2005-12-11 10:59:03

If you are looking for the distance along the surface of the earth.

Since 80° N above the equator and 70° S below the equator total 150° for the interior angle.  We can use:

s = rθ in rads or s = r π θ ÷ 180 in degrees  (s = arc length)

s = 6370(150π):div180 = 16676.6 km

If you want straight line distance between the two points then:

Since the interior angle of the apex is 150° and the radius is estimated to be 6370 we can use the law of sines.  The radius is constant and 180° - 150° = 30° tells us that the other angles are both 15°

x/sin 150° = 6370/sin 15°

So x = 6370 sin 150° / sin 15° ≈ 12305.9 km

Hope that helps.

MathsIsFun
2005-12-11 08:53:38

Careful ... it is a curved surface, so Pythagoras may not work  ...

mathsyperson
2005-12-11 03:26:29

In that case, it is definitely possible.

70S is around 5990 km below the equator and 80N is around 6280km above it.

If the 70S point is 6370km away from the equator and 5990km below it, then it must be √(6370² - 5990²) = 2167km to the left of the middle point.

Similarly, if the 80N point is 6370km away from the equator and 6280km above it, then it must be √(6370² - 6280²) = 1067km away from it.

Therefore, the 80N and 70S points are 5990 + 6280 = 12270km away from each other by latitude and 2167 - 1067 = 1100km away by longitude.

That means that they are √(12270² + 1100²) ≈ 12320km away from each other.

seren
2005-12-11 03:04:03

yep at equator - just my dodgy drawing :\$

mathsyperson
2005-12-11 02:55:11

I'm fairly sure that it can be worked out. Is the third point at the equator or just at an unknown place?

seren
2005-12-11 02:51:22

- > Is it possible to calculate the ? distance from the
information given?

It represents the earth and two places - one at 80 latitude North
the other at 70 latitude South